I don't think correlation vs causation is the right question. Loneliness was clearly rampant long before chatgpt showed up. The question is whether chatbots are capable of reducing people's loneliness. To me it feels self-evident that in the long run, they are far more likely to increase feelings of loneliness than reduce them.

For me, the only thing that can reduce loneliness is conversation with another conscious entity. Many, if not most, people are barely conscious so this is hard to find in the physical world. But I don't believe llms are conscious, so for me they are a complete dead end for reducing loneliness whatever other virtues the may have.